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Tempered stable Lévy motion driven by stable subordinator

Author

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  • Gajda, Janusz
  • Wyłomańska, Agnieszka

Abstract

In this article we propose a new model for financial data description. Combining two independent mechanisms, namely the tempered stable process and inverse stable subordinator, we obtain a new model which captures not only the tempered stable character of the underlying data but also such a property as periods in which the values of an asset stay on the same level. Moreover, we classify our system to the family of subdiffusive processes and investigate its tail behavior. We describe in detail testing and estimation procedures for the proposed model. In the last step we calibrate our model to the real data.

Suggested Citation

  • Gajda, Janusz & Wyłomańska, Agnieszka, 2013. "Tempered stable Lévy motion driven by stable subordinator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(15), pages 3168-3176.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:15:p:3168-3176
    DOI: 10.1016/j.physa.2013.03.018
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    Citations

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    Cited by:

    1. Hasan A. Fallahgoul & David Veredas & Frank J. Fabozzi, 2019. "Quantile-Based Inference for Tempered Stable Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 51-83, January.
    2. Gong, Xiaoli & Zhuang, Xintian, 2017. "American option valuation under time changed tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 57-68.
    3. Gong, Xiaoli & Zhuang, Xintian, 2017. "Pricing foreign equity option under stochastic volatility tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 83-93.
    4. Gong, Xiaoli & Zhuang, Xintian, 2017. "Measuring financial risk and portfolio reversion with time changed tempered stable Lévy processes," The North American Journal of Economics and Finance, Elsevier, vol. 40(C), pages 148-159.
    5. Jabłońska-Sabuka, Matylda & Teuerle, Marek & Wyłomańska, Agnieszka, 2017. "Bivariate sub-Gaussian model for stock index returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 628-637.

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